For blocked holes try and take a scrap piece of string, and place it under the main string that will be blocking the grommet in question on the outside of the racquet.
Now when you get back to that grommet you can grab that scrap string with needle nose pliers and either push down or pull up to open up the blocked grommet and it slides right in.This works real well! You have to plan for it.

You can weave your top 2 cross strings before you tension the outside mains, and that eliminates 1/2 the blocked holes.Again you have to plan ahead.

If you did not plan ahead:

You can also cut the tip to a sharp flat point as noted above but also then apply a very small amount of super glue to the tip, then spray it with super glue accelerator, so it sets up immediately and then it is stiffer to go through.

If an awl is absolute necessity, then take a stiff piece of poly, cut tip to point and you now have a plastic awl so not to damage a string.

Another trick you can do is take a basketball needle, cut the tip end and smooth it down nice and smooth. You can place that through the blocked grommet carefully thread the string through that needle, take the needle out and Bob's your uncle.Just be sure to place the needle on the proper side or racquet so you can take it out.

In reality just cutting the tip to a sharp and flat point and pushing through with small increments works 95% or more of the time,but the above tips may help if all else fails. Good luck jim